How to Convert Logarithmic Equation to Exponential Equation

How can we convert a logarithmic equation to an exponential equation?

Given logarithmic equation: log4a = -7

Converting Logarithmic Equation to Exponential Equation

To convert a logarithmic equation to an exponential equation, we need to understand the relationship between logarithms and exponents. In this case, we are given the logarithmic equation log4a = -7.

The given logarithmic equation log4a = -7 can be converted to an equivalent exponential equation by using the relationship between logarithms and exponents. This conversion allows us to express the same mathematical relationship in a different form.

By applying the basic rule of converting logarithmic equations to exponential equations, we rewrite the equation as 4-7 = a. Therefore, the equivalent exponential equation for log4a = -7 is a = 4-7.

Understanding how to convert between logarithmic and exponential forms of equations is essential in algebra and makes solving problems involving exponents and logarithms more manageable and versatile.

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